More Graphs and Displays

Stem-and-Leaf PlotsEach number is separated into a

STEM and LEAF component. The STEM is the leftmost digit(s).The LEAF is the rightmost digit.It’s important to include a key to

identify values. For example… Key: 15 | 5 = 155

Use the stem-and-leaf plot to list the actual data entries.

Make a stem-and-leaf plot:Ages of the top 30 highest paid CEOs

(Forbes Magazine).

64 74 55 55 62 63

50 67 51 59 50 52

50 59 62 64 57 61

49 63 62 60 55 56

48 58 64 60 60 57

Pie Chart (for Qualitative Data)A circle divided into sectors that

represent categories. The area of each sector is proportional to

the frequency of the category.

Find RELATIVE Frequency and multiply by 360o to get the central angle for each category.

Use a Pie Chart to display data2010 NASA budget request (in millions

of dollars)

Science, aeronautics, exploration

8947

Space Operations 6176

Education 126

Cross-agency support 3401

Inspector general 36

Pareto Chart (for Qualitative Data)Vertical bar graph in which the height of

each bar represents the frequency or relative frequency.

Bars are positioned in order of decreasing height, left to right.

EX: Make a Pareto chartUltraviolet indices for 5 cities at noon:

Atlanta

Boise

Concord

Denver

Miami

9 7 8 7 10

Scatter Plot (for Paired Data Sets)Paired data Ordered pairs. Plot on a coordinate plane.Independent variable on the x-axis.

EX: make a scatter plot:# of students per teacher

Avg teacher’s salary (in thousands$)

17.1 28.7

17.5 47.5

18.9 31.8

17.1 28.1

20.0 40.3

18.3 33.8

14.4 49.8

16.5 37.5

13.3 42.5

18.4 31.9

Measures of Central Tendency

Measure of Central Tendency:A value that represents a typical, or

central, entry of a data set. 3 most common are MEAN, MEDIAN,

and MODE

MEAN: sum of the data entries divided by n

MEDIANThe data entry in the MIDDLE.

List data from least to greatest.Find the middle value.(For even n, find the average of the 2

middle values)

MODEData entry that occurs MOST often

(highest frequency)

A data set may have no mode or have more than mode.

BIMODAL = 2 modes.

EX: Find mean, median, and mode for the data set.

Weighted MEAN: data values have different

weights.

EX: find the weighted mean

Mean of a Frequency Distribution

EX: Find the mean

Shapes of DistributionsDistributions may look ..

SymmetricUniformSkewed LeftSkewed Right

Symmetric

Uniform

Skewed Left

Skewed Right